I really need some help with this problem:

For each of the following linear operators T on the vector space V, determine whether the given subspace W is a T-invariant subspace of :

V=P(R), T(f(x)) = xf(x), and W=P2(R)

I was thinking that in order for this to be T-invariant, that means that it needs to be contained in W because T(W) needs to be contained in W.

Am I on the right track?